Microelectromechanical systems (MEMS), which are sometimes called micromechanical devices or micromachines, are three dimensional objects having one or more dimensions ranging from microns to millimeters in size. The devices are generally fabricated utilizing semiconductor processing techniques, such as lithographic technologies.
The use of MEMS to mix one or more fluids has numerous applications in industries ranging from chemical analysis, to printing, to medicine. As used herein, the term mix refers to combining two fluids, increasing the uniformity of a single fluid, decreasing the spacial or temporal gradients with respect to one or more fluid properties, or increasing small scale decomposed structure from large scale homogenous structure in a fluid.
As previously indicated, there are numerous applications for fluid mixing MEMS. For example, a device capable of mixing, and thereby processing, tens to hundreds of nanoliters of fluid would increase by two orders of magnitude the number of chemical tests that can be performed on a given volume of fluid. In printing, fluid-handling MEMS would allow for the mixing of inks "off-paper", thereby allowing for on-demand ink formation, increasing the print quality and decreasing the amount of ink required. In medicine, fluid-handling MEMS could be implanted under the skin, or incorporated in microfabricated needles, and programmed to mix and dispense assays according to current need or a pre-programmed schedule. Numerous additional applications exist for fluid-handling MEMS.
The ability to mix fluids thoroughly and in a reasonable amount of time is fundamental to the creation of fully integrated, "on-chip" MEMS fluid processing systems. Effective mixing of fluids requires that the fluids be manipulated or directed so that the contact area between the fluids is increased. In macroscopic devices this is generally done using turbulence, three-dimensional flow structures, or mechanical actuators. Since MEMS are fabricated in a planar, lithographic environment, design constraints mitigate against mechanical actuators. Further, the planar nature of MEMS prevents three-dimensional flow structures. That is, MEMS are essentially planar devices, including the X and Y axes defining the plane of the device. The design of structures in the third-dimensional Z axis (or vertical axis rising from the plane defined by the X and Y axes) is constrained by lithographic techniques. For example, lithographic techniques limit the Z axis structures to uniform shape and depth throughout the device. As a result, the Z axis dependence of the flow field will be uniform (e.g., parabolic) throughout the planar device. A flow with uniform Z dependence is referred to as planar flow. It is difficult to achieve mixing in this context.
The size and proportions of MEMS generally preclude relying on either turbulence or diffusion alone as mixing mechanisms. The size of fluid chambers in a MEMS can range from the picoliter, (10 .mu.m).sup.3, to the microliter, mm.sup.3, range. Though fabrication constraints allow for picoliter chambers, few commonly used fluids are concentrated enough to be useful in such quantities. An upper bound on volumes of about 50 .mu.l is set by the size of a typical device (10 mm.times.10 mm.times.500 .mu.m). Process volumes in the 100 nanoliter range allow multiple chambers to be fabricated on one die, yet provide sufficient fluid for many applications.
Turbulence occurs in flows characterized by high Reynolds numbers, defined as EQU Re=(U.delta.)/v, [1]
where U is a characteristic velocity, .delta. is a length scale, and v is the kinematic viscosity (1 mm.sup.2 /s for water). The appropriate length scale, typically the channel height, will in general be smaller than 500 .mu.m. Assuming the highest velocity to be experienced for on-chip flows is one die length per second (U=10 mm/s), an upper bound on the Reynolds number is Re=5, with typical values being much lower. As turbulence in channel flow occurs only for Re&gt;2000, on-chip flows are expected to be laminar, and thus turbulence is not available as a mixing mechanism. Moreover, flows with Re&lt;&lt;1, known as creeping flows, are symmetric and reversible. In this regime, a flow moving past an object will reconstitute itself, passing by the object unchanged, and "mixing" caused by a given set of manipulations to the fluid can be undone simply be reversing the set of manipulations. This precludes the use of barrier-fields, complex geometries, and severely limits the usefulness of mechanical actuators.
Similarly, the size and shape of MEMS limit the usefulness of diffusion as a sole mechanism for mixing. As it is difficult to place two fluids on top of each other in a planar MEMS, the length over which diffusion must act will be the in-plane dimension of the fluid chamber. Using Fick's equation, a diffusion mixing time scale, T.sub.D can be formed EQU T.sub.D =L.sup.2 /k, [2]
where L is the relevant mixing length, and k is the Fickian diffusion constant (k=10.sup.3 .mu.m.sup.2 /s for salt in water, for example). Using L=1 mm, T.sub.D =10.sup.3 seconds=16.6 minutes. Even for L=100 .mu.m, T.sub.D =10 seconds. Such mixing times are generally too slow to rely on diffusion for effective mixing.
It would be highly desirable to overcome the foregoing difficulties associated with mixing fluids in a MEMS, and thereby provide a MEMS with improved mixing capacity.